modal logic

Overview of logics

alethic, deontic, axiological, epistemic, doxastic, boulomaic modal operators ...

Kripke system, $\mathbf{K}$

(Saul Kripke)

$\mathbf{K}$ results from adding the following to the principles of propositional logic.

• Necessitation Rule: If $A$ is a theorem of $\mathbf{K}$, then so is $\Box A$.
• Distribution Axiom: $\Box ( A \to B ) \to ( \Box A \to \Box B )$ .

#incomplete

S5 modal logic

See also

• modal collapse

References

1. https://plato.stanford.edu/entries/logic-modal/
2. https://plato.stanford.edu/entries/logics-for-games/
3. https://ai.stanford.edu/~epacuit/classes/modal-spr2012/ck-modal.pdf
4. Michael C. Nagle, S. K. Thomason. "The Extensions of the Modal Logic K5", The Journal of Symbolic Logic, Vol. 50, No. 1 (Mar., 1985), pp. 102-109 (8 pages) https://doi.org/10.2307/2273793
5. Linh Anh Nguyen. "Sequent-like Tableau Systems with the Analytic Superformula Property for the Modal Logics KB, KDB, K5, KD5". https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=d35d37361c45213917f0f9644d790c0e87d1ef54
6. Olivier Gasquet, Andreas Herzig, Bilal Said, François Schwarzentruber. "Kripke’s Worlds An introduction to modal logics via the tableau method", ESSLLI 2010, Institut de Recherche en Informatique de Toulouse (IRIT), Université de Toulouse, 2010. https://www.irit.fr/~Andreas.Herzig/Cours/CTableaux/Esslli10.pdf
7. R. Zach, Boxes and Diamonds: An Open Introduction to Modal Logic. S.l.: Independently published, 2019. [Online]. Available: https://bd.openlogicproject.org/
8. https://en.wikipedia.org/wiki/Modal_operator
9. https://iep.utm.edu/modal-lo/